What is the ruling on the ablution of one from whom blood exits from his nose or a wound?
Blood flowing from a wound or a nosebleed does not invalidate ablution. However, performing ablution is recommended to avoid scholarly disagreement with those who make ablution obligatory after blood flows. And Allah the Almighty knows best.
What is the meaning of the word aqiqah?
All praise is due to Allah, and may peace and blessings be upon our Master, the Messenger of Allah.
The 'aqīqah in its linguistic sense refers to the hair upon the head of a newborn at the time of birth.
In its Sharī'ah sense, it refers to the livestock that is slaughtered on behalf of a newborn child.
And Allah Almighty knows best.
What is the ruling of Islamic Law on a person who abandons prayer after reaching puberty—is he required to make them up?
All praise is due to Allah, and peace and blessings be upon our master, the Messenger of Allah.
Making up missed obligatory prayers is an Islamic duty just as performing them in their proper time is obligatory, and taking care of them takes precedence over performing voluntary prayers. This is established by the practice of our Supreme Prophet (peace and blessings be upon him) when the polytheists distracted him on the Day of the Trench from performing the Asr prayer, so he made it up afterward, as well as the Hadith: "Pay Allah what is due to Him, for Allah is most deserving of fulfillment." (Recorded by Al-Bukhari)
Furthermore, it is valid to make up missed prayers at any time.
Whoever has missed a number of prayers and does not know their exact count, it is obligatory upon them to sincerely repent and exert their utmost effort to estimate their number. If they are unable to determine the exact count, they should base it on what is most probable according to their best judgment. They should then make them up gradually; if one performs one missed prayer alongside every current obligatory prayer, the matter becomes easy and manageable, and with the passage of time, one will complete what is owed, Allah willing. And Allah Almighty knows best.
What should a person, who doubts the validity of his Wudu, or over performs it, do?
One who doubts the validity of his/her Wudu while performing it should redo it until he/she is certain of having attained purity. But, if doubt was after having performed Wudu, then he/she should not pay attention to that as doubt after the end of an act of worship does not count. This is of course in case doubt was within the reasonable limits since once it goes beyond that, it becomes a whispering of the Shaytaan (devil) which he/she should ignore as the Wudu is valid.